Heat conduction equation
- To: mathgroup at smc.vnet.net
- Subject: [mg32848] Heat conduction equation
- From: "Maurizio Tomasi" <zio_tom78 at hotmail.com>
- Date: Fri, 15 Feb 2002 02:49:50 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello to everybody.
I am trying to find a solution to the heat conduction equation (in one
dimension) by using the Fourier transform. The equation has the
d T d T
C ------ + q delta(x) - k rho ----- = 0
2 d t
and the Cauchy condition is
| i omega t
T (x=x1, t=0) = | c (omega) e d omega
(at some point x1 the temperature must have a pre-defined spectral
shape). The Dirac delta in the equation represents a source of heat
placed at x=0.
Could somebody give me a reference or an hint about possible analytical
solutions of this equation (in terms of generalized functions)? I
managed to solve it by ignoring the second or the third term, but now I
need a *general* solution.
Thanks in advance
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